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Centripetal Force – Facts you must know if you are a PHYSICS student !


Centripetal force and a few must-know facts

Centripetal force and its concepts have always been in the favorites list of the students. Still we find many misconceptions and assumptions in their mind, around the fundamental concepts of this force.

In this post we will try to discuss on few such pointers, which will certainly help you to understand centripetal force in a better way !

Definition-What is centripetal force? Centripetal force is a force which acts on a object rotating in a circular path. And this force acts in the direction towards the centre of the circle.This is the force which enables an object to continue its motion in a circular path.

Examples-We see many instances of the centripetal force being applied in the nature. Applying the concepts of this force many devices like washing machine have been designed.

Students of fundamental physics must have a strong grasp on the concepts of this centripetal force. Here find a few important pointers with detailed explanation of each which you will certainly like!

centripetal force

Horizontal circular motion and role of Gravity on the rotating object, irrespective of the centripetal force

 

Let’s tie a rock to one end of a string and other end of the string is tied with a finger. Then start to rotate the rock with the help of the string in a horizontal plane. The rock starts moving in the horizontal circular track without any intention to drop towards the earth.

So how is this possible? How come it’s avoiding the effect of gravity?

Let’s find out. We all know that the gravity works towards the centre of the earth. As the rock is maintaining a circular path in a horizontal plane, its motion is at a right angle with the line of action of the gravity.

So do you think gravity has any effect on the rock piece rotating there?

centripetal force diagram1

Diagram-1

We can quickly check from the definition and formula of work done. Work done depends on the Cosine of the angle between the line of force and the displacement of the object.

But here what is the angle between the rotating rock and the line of gravity? Yes ! It’s 90 degree. And cos 90 degree is zero.

What does this mean? This means work done on the rotating rock by the gravitational force of earth (gravity) is  ZERO. Therefore the gravity has no effect on its motion. Reference: Diagram-1

Centripetal Force & Newton’s First Law of Motion

 

How and Why Newton’s Law has come into this scenario? Continuing with what we were discussing, if the string is released suddenly, then what would happen?

The rock would fly off at a tangent to the circular path it was maintaining so far. It’s the demonstration of Newton’s First Law of Motion. How is that law being demonstrated here? Let’s discuss.

As per the Law, an object with uniform velocity will continue to move in a straight line with the same velocity, if net force applied on it is zero.

But here we see as long as the string is intact, the tied rock can be given a circular motion. During this motion at every instance its direction is changing. That means at every instance its velocity is changing! This again points to the fact that this motion is under acceleration!

So what can we derive from here? Yes, you are right!

There must be some force acting on the tied rock which is helping it to change its velocity at every moment. From the motion of the tied rock it’s evident that the force is somehow working towards the center of the circular path.

And a special name is given to this force acting on a rotating object and directing towards the centre of the circular path. It’s called Centripetal Force. ( Reference: Fc shown in Diagram-1 )

centripetal force

Now how is this centripetal force being applied on the rock?

Of course, it’s being transferred from the finger to the rock and this transfer is happening via the string only.

Who is supplying this centripetal force here? The finger. That’s why when the string is released or the string is torn this force can’t pass to the rock any more.

This is the instance when Newton’s 2nd Law comes into play. As there is no force (net force) on the rock so it will continue along its last direction on the circular path. And direction is actually the tangent to that point on the circular path.



Centripetal Force – Who or What is supplying this?

 

1) In the above example a rock is rotated in horizontal plane with a string tied with a finger. Here the finger supplies the required centripetal force that makes the rock rotate. There are a few other instances when the supplier of this force varies case to case.

2) Electron orbits the nucleus in an atom. Electrical attraction force generated between an electron and the nucleus, supplies the centripetal force on the electron.

centripetal force-thorium-atom-circular motion
3) A car or a bike taking a circular bend – The Frictional force between the tires and the road supplies the required Centripetal force. (As it is a frictional force so certainly it has a maximum limit, beyond which balancing in a bike at a circular bend won’t be possible. It’s a different story, will take this in a separate post)

centripetal force-circular bend-friction

4) Satellite revolves around the earth. Here Gravitational Attraction between the earth and the satellite supplies this centripetal force.

centripetal force between earth and moon

To note that this centripetal force is a real force.

 Centripetal Force – Factors

 

The formula of Centripetal force is F= mω2R, where m is the mass of the object, ω is the angular velocity and R is the radius of the circular path.

1) An object with more mass would be requiring less angular velocity and smaller radius of circular motion, to maintain it circular motion.

2) If R is high, even a lower angular speed can keep an object rotating in a circular path.

3) If R is too small, then angular velocity has to be at higher side to compensate the small R and generate the necessary Centripetal Force required to continue circular motion.

centripetal force

Centripetal Force and Centrifugal Reaction, Newton’s 3rd Law

 

As per Newton’s 3rd Law, Centripetal Force must be having an equal and opposite reaction force.

Yes, it has. It’s called Centrifugal Reaction. Please note that it’s not same as Centrifugal Force. Concept of centrifugal force is completely different and we will take that one shortly.

Coming back to Centrifugal Reaction ! When we rotate a piece of rock with our finger through a tied string, then the finger also feels a force which is applied by the rotating rock. This is Centrifugal Reaction force.

Centripetal Force and Centrifugal Reaction

Diagram-2

Now as its direction is opposite to the Centripetal force (finger feels a force which tries to drag it outwards, away from its central position) , its Centrifugal and as it’s a reaction force, so we call it as Centrifugal Reaction force. (CR in Diagram 2)

Centripetal Force Vs Centrifugal force

 

Centrifugal Force – a pseudo force, it’s not real like centripetal force

Centripetal force is a real Force because it evolves due to mutual interaction of objects or masses.

But Centrifugal force is felt only within a Rotating Frame of Reference.

If a person shares the same frame of reference of a rotating object, then that object will apparently look like a static object to that person. The person within a rotating frame of reference will never understand the reason of Centripetal Force being applied because for him that frame of reference is static and for something static there is no need of any force to be applied.

Rather he will feel as if some external force is being applied which is pulling the entire system away from the central position and there is another force directed towards the centre which is balancing the first one.

Centripetal Force-Centrifugal force-rotational frame of reference

Diagram-3

When passengers travel in a bus and the bus takes a sharp turn, then the passengers feel a thrust in the opposite direction. Here the bus is an example of Rotating Frame of Reference and the passengers within that that frame of reference feel a pseudo force, an unreal force! (see Diagram 3)

This pseudo force is called Centrifugal Force.

The road beside the bus is a static frame of reference. A person standing in that static frame will never reciprocate the presence of centrifugal force for that bus, to him the movement of the passengers is just because of directional inertia.

Washing Machine and the Centripetal Force

Let’s see how concepts of centripetal force have been intelligently implemented in a common household machine. Yes, I am talking of Washing Machine.

As clothes are put inside the drum and drum is filled with water, circular motion sets in to the drum.

centripetal force-washing machine

Circular motion of the drum transmits similar motion to the clothes as well. But as the clothes are not physically attached to the centre of the drum, they don’t get any centripetal force to continue the circular motion uniformly.

As a result they tend to move in a straight line tangent to the circular path. But they face the drum body on their way, hit it forcefully and revert back. Rotating drum again injects circular motion to the clothes and this cycle continues.

But this doesn’t happen to the water droplets in the clothes. As the clothes hit the drum body, as described above, the water droplets make their way to outside of the drum, through the holes on the drum body. And the clothes get rid of the water by the time washing cycle completes.

centripetal force-circular motion

Hope you enjoyed. We will discuss more in this line ! Pls see the ‘Study Suggestions‘ and the VIDEO below!

 Centripetal force & Related Study Suggestion:

1) Critical Velocity in Circular motion in vertical plane

2) Circular Motion and its relationships with linear motion

3) Wikipedia

Centripetal Force – an Outstanding Video for you

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